Prepared by: Ronnie Asuncion WAVEGUIDES Prepared by: Ronnie Asuncion

What is waveguide? Hollow conductive tube Usually rectangular in cross section but sometimes circular or elliptical Electromagnetic (EM) waves propagate within its interior Serves as a boundary that confines EM energy The walls of it reflect EM energy Dielectric within it is usually dehydrated air or inert gas EM energy propagate down in a zigzag pattern

Rectangular and circular waveguides What is waveguide? Generally restricted to frequencies above 1 GHz Rectangular and circular waveguides

Why use waveguide? Parallel-wire transmission lines and coaxial cables cannot effectively propagate EM energy above 20 GHz Parallel-wire transmission lines cannot be used to propagate signals with high powers Parallel-wire transmission lines are impractical for many UHF and microwave applications

Rectangular Waveguide Most common form of waveguide For an EM wave to exist in the waveguide it must satisfy Maxwell's equation Note: A limiting factor of Maxwell’s equation is that a transverse electromagnetic (TEM) wave cannot have a tangential component of the electric field at the walls of the waveguide EM wave cannot travel straight down a waveguide without reflecting off the sides

Rectangular Waveguide The TEM wave must propagate in a zigzag manner to successfully propagate through the waveguide with the electric field maximum at the center of the guide and zero at the surface of the walls

Phase and Group Velocities In parallel-wire transmission lines, wave velocity is independent of frequency, and for air or vacuum dielectrics, the velocity is equal to the velocity in free space In waveguides the velocity varies with frequency Group and phase velocities have the same value in free space and in parallel-wire transmission lines The velocities are not the same in waveguide if measured at the same frequency At some frequencies they will be nearly equal and at other frequencies they can be considerably different

The phase velocity is always equal; to greater than the group velocity The product of the two velocities is equal to the square of the free space propagation speed Vg Vph = c^2 where: Vph = phase velocity (meters/second) Vg = group velocity (meters/second) c = free space propagation speed = 300,000,000 (meters/second)

Group Velocity The velocity of group waves The velocity at which information signals of any kind are propagated The velocity at which energy is propagated Can be measured by determining the time it takes for a pulse to propagate a given length of waveguide

Phase Velocity The apparent velocity of a particular phase of the wave The velocity with which a wave changes phase in a direction parallel to a conducting surface, such as the walls of a waveguide Determined by increasing the wavelength of a particular frequency wave, then substituting it into the formula: Vph = f λ where: Vph = phase velocity (meters/second) f = frequency (hertz) λ = wavelength (meters/second)

Phase Velocity may exceed the velocity of light Phase velocity in waveguide is greater than its velocity in free space Wavelength for a given frequency will be greater in the waveguide than in free space

Phase Velocity Free space wavelength, guide wavelength, phase velocity and free space velocity of electromagnetic wave relationship: λg = λo (Vph / c) where: λg = guide wavelength (meter/cycle) λo = guide wavelength (meter/cycle) Vph = phase velocity (meters/second) c = free space velocity (meter)

Cutoff Frequency and Cutoff Wavelength Cutoff Frequency - minimum frequency of operation - an absolute limiting frequency Cutoff Wavelength - maximum wavelength that can be propagated down the waveguide -smallest free-space wavelength that is just unable to propagate in the waveguide

Cutoff Frequency and Cutoff Wavelength The relationship between the guide wavelength at a particular frequency is: λg = (c) / [(f^2)-(fc^2)]^(1/2) where: λg = guide wavelength (meter/cycle) fc = cutoff frequency (hertz) f = frequency of operation (hertz) Determined by the cross-sectional dimension of the waveguide

Cutoff Frequency and Cutoff Wavelength fc = c/2a = c/λc Where: fc = cutoff frequency a = cross-sectional length (meter) λ = cutoff wavelength (meter/cycle)

Modes of Propagation Electromagnetic waves travel down a waveguide in different configurations called propagation modes There are two propagation modes: - TEm,n for transverse-electric waves - TMm,n for transverse-magnetic waves TE1,0 is the dominant mode for rectangular waveguide At frequencies above the fc, higer order TE modes are possible

Modes of Propagation It is undesirable to operate a waveguide at frequency at which higher modes can propagate Next higher mode possible occurs when the free space λ is equal to a A rectangular waveguide is normally operated within the frequency range between fc and 2fc

Characteristic Impedance Zo = 377/{1-(fc/f)^2} = 377(λg/ λo) Where: Zo - characteristic impedance (ohms) fc - cutoff frequency f - frequency of operation

Impedance Matching Reactive stubs Capacitive and inductive irises

Circular Waveguide Used in radar and microwave applications The behavior of electromagnetic waves in circular waveguides is the same as it is rectangular waveguides Are easier to manufacture than rectangular waveguides Disadvantage is that the plane of polarization may rotate while the signal is propagating down it.

Circular Waveguide Cutoff wavelength, λo λo = 2πr/kr where: λo = Cutoff wavelength (meters/cycle) r = internal radius of the waveguide kr = solution of Bessel function equation TE1,1 is the dominant mode for circular waveguides the cutoff wavelength for this mode is: λo = 1.7d d = waveguide diameter

Flexible Waveguide Consist of spiral wound ribbons of brass or copper Short pieces of the guide are used in microwave systems when several transmitters and receivers are interconnected to a complex combining or separating unit Used extensively in microwave test equipment

Flexible Waveguide